Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 27, 2017; final manuscript received January 4, 2018; published online February 2, 2018. Assoc. Editor: Weinong Chen.

Abstract

Coefficients of restitution (CoR) is used to scale the kinetic energy dissipation, which is a necessary parameter for discrete element modeling simulations of granular flow. Differences from the collision of spherical particles, CoRs of spheroid particle are affected not only by materials, particle size, and impacting velocity, but also by the contact inclination angle of the particle. This article presents our experimental investigation to measure the velocities of translation and rotation using high-speed camera and calculate the CoR in normal direction of prolate spheroid particles impacting flat targets. The results show that this CoR of a prolate spheroid particle is composed of two parts, translation and rotation. The effect from the contact inclination angle is not obvious for a given velocity. When the contact point is close to a pole, the first part plays a major role. On the contrary, the second part dominates the CoR, when the contact point is close to the equator. A dimensionless number, e*, is defined to scale the proportion of velocity due to rotation in the total rebound velocity at the contact point. The relationship between the contact inclination angle, ϕ, and e* for 25 deg < ϕ < 90 deg is given in this article.

The radii of curvatures for a prolate spheroid in the form of x2+y2/a2+z2/c2=1. APB̂ is the meridian arc between two poles A and B; r′ is the radius of curvature for this curve at point P; GPĤ is normal to APB̂ at point P, and r″ is the radius of curvature for arc GPĤ at point P. r′ and r″ are the principal radii of curvature at point P.

eT of spheroid particle #6 with different contact inclination angles, ϕ, and data fitting using the power law, Eq. (20), where ζ = 0.243, same as that for the power curve in Fig.8. The symbols have the same meaning as those in Fig. 10.

A sketch of a second collision. (a) before the first collision, c is the first collision point; (b) after the first collision; and (c) second collision happens due to a high angular velocity ωr, and c′ is the second collision point.

Return to: The Coefficient of Restitution of Spheroid Particles Impacting on a Wall—Part I: Experiments

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